Endgame positions with just one king on the board may be very rich. Has any analysis of simple positions done? Maybe even tablebases for small numbers of pieces?
There are some existing problems with no White king. For example, helpmate in 7 (Buchanan & Foster - TPS 2020). But the question here concerns endgame studies.
[FEN "1n2k3/3pp3/8/8/8/8/4P3/8 w - - 0 1"]
The positions are illegal, but there's no problem playing forwards. Only one side can be mated, but imbalance of force is a part of many fascinating legal endgames. They may also occur in e.g. long games of Horde Chess.
I emailed chess theorist, John Beasley, who seemed the person most likely to have explored this area, if anyone had. But he has no idea.